Physics - Simple Harmonic Motion

[nyyfan0729]

A block of mass 0.5kg moving on a horizontal frictionless surface at 2.0 m/s collides with and sticks to a massless pan attached to the end of a horizontal ideal spring whose spring constan is 32 N/m.
a) Determine the function for x(t), the displacement from equilibrium position as a function of time.
I got this to be x(t) = .25sin(8t)

b) What is the period T, of the subsequent oscillations?
I got the period to be .785 sec
I NEED HELP WITH C AND D, WHAT DO I DO?
c) What is the kinetic energy of the mass 4.0 sec after it collides with the spring?

d) What force is exerted by the spring on the block at t=1.2 sec? Which way is the block moving? Explain

 

[gulsen]

If you have x(t), you can get all of the answers our of it. For instance, your w seems to be 8, which is the angular speed and equal to 2 \pi / T.
For KE, you can simply get the 1st time derivative of x(t), and you have v(t), and calculate mv(4)^2/2.
As for the force, 1st time derivative of v(t) gives a(t), and all you need seems to be ma(1.2). Compare the signs of position and force at t=1.2, and you can conclude whether if they're pointing at the same direction or not. Finally, check out the sign of v(1.2) and happy end :)